What about diverting the desire to give gifts into something both fun and cheap/unpressured? E.g., an office Secret Santa, a Yankee swap, or the like? We have done the secret Santa thing, where people could choose to participate or not, and with a hard cap of $15; we do it over a pizza lunch in the office conference room -- but the idea was that they were funny/appropriate gifts vs. trying to do something seriously nice. More recently, we changed it to the same idea, but the gifts went to a children's charity. DH's office does a Yankee swap that turns into a multi-hour laughing fit, as everyone fights over something stupid (usually the liquor). So everyone gives something, everyone gets something, everyone has a good time and gets to celebrate, but there's no financial pressure or awkward boss/staff dynamics.
And then you as boss could still give everyone a small bonus or gift card to show your appreciation for their work.